Environmental Regulation in a Mixed Economy
Guangliang Ye
Jinhua Zhao†
September 2013
ABSTRACT
Many developing countries are mixed economies in which public and private firms engage in
Cournot competition. We show that some fundamental results in environmental economics fail to
hold in these economies: more stringent environmental regulation does not necessarily reduce
pollution levels, and the equivalence between environmental taxes and standards breaks down. The
driving force lies in the endogenous objective functions of public firms manifested through the career
choices of the public firm’s CEO. Instruments that can induce the CEO to choose a public career tend
to be welfare dominant.
Keywords: Environmental regulation, emission taxes, emission standards, mixed oligopolies,
developing countries
JEL Codes: Q58, L13, L32
†
Ye: Hanqing Advanced Institute of Economics and Finance, School of Economics, Renmin University of China. Zhao:
Department of Economics, Department of Ag., Food and Resource Economics, Environmental Science and Policy
Program, Michigan State University, 110 Marshall-Adams Hall, East Lansing, MI. Email: jzhao@msu.edu. Voice:
1-517-353-9935.
1
I. Introduction
Developing nations such as China and India are increasingly becoming important players in
global environmental protection due to rapid economic growth, large population base and fragility of
some of their domestic ecosystems. When pollution is global as in the case of greenhouse gas
emissions, these nations are critical in ensuring the success of international mitigation efforts. Solving
global externalities requires better understanding of the environmental protection incentives and
mechanisms within developing nations.
Many developing nations themselves are imposing more environmental regulation as the
domestic income levels rise and as their citizens increasingly recognize the damages of pollution.
Some of the environmental standards in China are as strict as those in the U.S., and both China and
India have witnessed improvements in the stringency and breadth of their environmental regulation
(Chang and Wang, 2010; Sawhney, 2004). More stringent environmental regulation might be one
factor contributing to the widely observed environmental Kuznets curve (Grossman and Krueger,
1995).
Environmental economics research has made significant contributions to environmental policy
making in industrialized nations (Hahn, 2000). One of the key contributions is the choice of
environmental instruments. For instance, environmental taxes and standards are equivalent under
certainty, with the optimal choice largely driven by firm heterogeneity, transaction costs and
innovation incentives (Jaffe and Stavins, 1995; Jung et al. 1996; Zhao, 2003). Overall the research
shows that market instruments such as taxes and tradable emission permits perform better than
command-and-control approaches such as standards in the context of industrialized nations (e.g.,
Stavins, 2003).1
In this paper, we study to what extent major findings on environmental regulation and in
particular on environmental policy instruments are “portable” to developing countries. If the only
difference between developing and developed nations is income levels, then it is fairly
1
The dominance of market instruments is sensitive to the institutional settings in which environmental regulations are
implemented. For instance, Endres (1997) and Endres and Finus (2002) show that when heterogeneous nations negotiate
an international environmental agreement, an emission reduction standard agreed upon by the negotiating nations might
dominate an emission tax.
2
straightforward to extend the findings to developing nations: we need to adjust for the different
preferences towards the environment and possibly for different risk attitudes due to the lower income
levels. At least theoretically it is not hard to account for simple institutional differences such as
adjusting for imperfect enforcement of environmental regulations (Montero, 2002). We expect that
major findings will remain valid in developing nations since the mechanisms through which
regulations affect economic activities in markets work similarly despite differences in levels of
economic development.
However, developing nations are different from developed market economies in another
important aspect, which might render current findings on environmental regulation less relevant for
the former: many developing nations are characterized by mixed economies or mixed oligopolies,
markets where state owned firms are major players with strong presence of private firms. We
investigate the implications of this unique market structure for optimal choices of environmental
policy instruments.
A mixed oligopoly describes a situation where public and private firms compete against each
other in a single market. The literature on mixed economies has focused mainly on the welfare
implications of the presence of public firms, recognizing early on that social welfare maximizing
public firms can regulate or “discipline” private oligopolies (Merill and Schneider, 1966). The
welfare effects are “mixed:” DeFraja and Delbono (1989) show that the presence of a public firm
increases welfare when there are only a few Cournot rivals but decreases welfare when the number of
rivals is large. The effects are ambiguous even when strategic delegation is allowed (Barros 1995,
Matsumura 1998, Jansen, Lier and Witteloostuijn 2006, Du, Heywood and Ye 2013) and the role of
leadership is accounted for (Fjell and Heywood 2004, Heywood and Ye 2009).
A related characteristics of mixed economies is that CEOs of public firms (and for that matter,
most of the upper level administration of public firms) are often former or future government officials.
In the case of China, a CEO typically carries a “rank” in the government system.2 Successful
performance at a public firm can be rewarded by promotion in government official ranks.
Alternatively, the CEO can choose to pursue careers in the private sector. We show that the
2
For instance, the CEO at a national iron and steel corporation usually carries the rank at the vice minister level.
3
endogeneity of CEO career choices is the major factor driving the performance of regulatory
instruments.
Public firms, often by government mandates, pursue objectives that go beyond pure profit
maximization. The vector of objectives might include social responsibilities such as job creation
(Shleifer and Vishny1994), income redistribution (Zeckhauser and Horn 1989, pp. 12–14), and
consumer welfare (Matsumura 1998). In the arena of environmental protection, public firms might be
required to take leadership roles in carrying out the government’s environmental objectives
(Mascarenhas,1989), and to do more in reducing their emissions (Darnall and Edwards, 2006). The
additional requirements often create dilemmas for the CEOs of these firms. On the one hand, they
have incentive to meet the social responsibilities if they will pursue a public career. On the other hand,
they might be concerned about reduced profitability when meeting the social responsibilities if they
will pursue a private career. A CEO who chooses a public career will put more weight on social
welfare compared with one who chooses a private career. We allow both the weight on social welfare
and the CEO’s career objective to be endogenous and to be affected by environmental regulation.
Environmental regulation often influences the public and private firms differently: if a public
firm has already been doing more in environmental protection, regulation will tilt the competition to
its advantage. The effects also depend on the regulatory instrument: while under a binding standard,
both public and private firms might undertake the same level of abatement, the public firm might
abate more under an environmental tax due to its preference for social welfare and the fact that tax
revenue contributes to social welfare. The impacts naturally depend on the public firm’s weight on
social welfare, and thus on the CEO’s career objective. More importantly, the CEO’s career objective
can also be changed by environmental regulation. If the CEO switches from a public career objective
to a private career objective due to the regulation, the public firm’s incentive to abate will decrease:
environmental friendly regulation could have perverse effects on the environment. A contribution of
this paper is to study the endogenous choices of the nature of the public firm, determined to a large
extent by the CEO’s career objectives, which in turn are affected by environmental policies. We show
that the endogeneity leads to non-monotonic effects of environmental regulation: a higher tax or more
stringent standard does not always lead to lower net emissions. Further, the equivalence between
4
taxes and standards breaks down: there are cases in which pollution levels induced by one instrument
cannot be achieved by the other instrument.
Although our focus on mixed economies is motivated by experiences of developing countries,
the presence of strong public firms is by no means limited to developing countries only. It is not
uncommon for an industrialized nation to have some sectors that are mixed. The US package delivery
sector, for example, is dominated by the USPS, a public firm, and Fedex and UPS, two private firms.
Our results are applicable to environmental regulation in such mixed sectors in industrialized nations.
The paper is organized as follows. Section II sets up the model and presents results of a Cournot
duopoly under pollution taxes. Section III examines the consequences of emission standards. Section
IV compares the performances of pollution taxes and emission standards. Section V provides
concluding remarks.
II. A model of mixed economies
Consider an economy consisting of one public firm indexed by 0 and one private firm indexed
by 1 competing in a single domestic market. Both firms produce a homogeneous good and share the
same production cost function, C(q)  kq , where k  0 is the (constant) marginal cost. The firms face
a linear inverse demand function P (Q )  a  Q where Q  q0  q1 and qi is the output of firm i, i=0,
1. The linearity assumption of the cost and demand functions, fairly standard in the mixed economy
literature (Pal 1998, White 2001 and 2002, Matsumura 2003), greatly simplifies our analysis; we will
discuss their implications and the generality of our results in Section V.
Each firm generates emissions that are proportional to its output level. Without loss of
generality, we assume that one unit of output generates one unit of emission so that firm i’s gross
emission is qi . The firm can abate its emission by a proportion of i , i.e., from qi to
ei  (1   i )qi at a unit cost of c. The government imposes a pollution tax at rate  , so that firm i has
to pay an environmental tax Ti (qi )   (1   i )qi . Firm i’s profit is
5
1
πi  qi (a   qi )  kqi  c i qi   (1   i ) qi ,
i 0
i  0,1
(1)
We assume that a  k  max{ , c}  0 : production is “desirable” regardless of a firm’s pollution
abatement decisions.
The social welfare consists of four components: consumer surplus, firm profits, tax revenue, and
1
the (linear) environmental damage D ( E )   E where E   ei :
i 0
Q
1
W  0 P(t )dt  P(Q)Q   (πi  Ti )  D( E )
(2)
i 0
We assume   c : pollution abatement is socially desirable.3
We allow pollution tax  to differ from marginal damage  . While the private firm’s
objective is to choose output q1 and abatement 1 to maximize  1 given in (1), the public firm is
often required by government mandates to balance its profit with social welfare. That is, the public
firm maximizes a weighted sum of its profit and the social welfare,
G  (1   )W   0
(3)
where 0    1 is the weight on profit.4
In mixed economies, a public firm’s CEO often has his or her own objectives that are divergent
from the mandated objectives of the public firm. This leads to a principal-agent problem when the
goals of the two differ. For instance, CEOs usually intend to spend on activities that benefit them,
such as growing the firm beyond efficient scale, gaining market shares, etc. We allow the CEO to
have his own objective which will affect how he balances the firm’s profit with the social welfare.
3
In fact, given the linearity assumptions, the socially optimal decision involves full abatement:
assume a  k  3
 2  0 to guarantee that all equilibrium outputs are nonnegative.
 1.
We further
Parameter  also represents the partial privatization ratio in the literature on privatization in mixed oligopolies
(Matsumura, 1998).
4
6
Specifically, the CEO chooses the profit weight  to maximize his own payoff, which depends on
the type of career he would like to pursue in the future:5
 f ( 0   1 ) if private career
Max U  
{ }
if public career
 g (W )
(4)
with f '  0, f ''  0 , g '  0 and g "  0 . If the CEO plans to pursue a private career, his future job
opportunities and market value depend on the public firm’s performance (profit level) relative to its
competitor, the private firm. However, if he would like to pursue a public career, he will be evaluated
on how well the public firm has served the government objective (of maximizing the social welfare),
and his future payoff is determined by social welfare W.6
The game has three stages. In stage one, the public firm’s CEO decides which type of career to
pursue in the future. Given the chosen career path, the CEO chooses weight  in the public firm’s
objective function in stage two. In stage three, the public and private firms engage in Cournot
competition. We solve for the subgame perfect Nash equilibrium using backward induction.
II.1 Subgame perfect Nash equilibrium
Given pollution tax  and the public firm’s profit weight  , the public and private firms
simultaneously choose their abatement and output levels. Since the abatement technology is linear, a
firm conducts either no abatement or full abatement. If the tax rate is higher than the unit cost of
abatement, both firms fully abate:  0  1  1 . If   c , the private firm does not abate, i.e., 1  0 ,
but the public firm might still abate if its weight on social welfare is sufficiently high: 0  1 if and
5
The degree to which the CEO dominates firm decisions is determined by managerial discretion, or the CEO’s latitude
of actions (Hambrick and Finkelstein, 1987), and varies across industries (Hambrick and Abrahamson, 1995). As long as
CEO preferences substantially influence the firm’s behavior, our results are robust to varying the degree of managerial
discretion.
6
An alternative interpretation of this setup is that the public firm’s manager maximizes (3) choosing the output and
abatement levels, with the weight  chosen by the CEO. Both the government mandate and the CEO can influence the
manager’s objective: the government mandates the structure of the public firm’s objective with the CEO influencing the
specific weights.
7
only if    I 
 c
. The threshold profit weight  I is such that the public firm is indifferent
 
between abating and not abating when    I . In this case we assume that it chooses not to abate.
The following proposition summarizes the equilibrium abatement and output levels.
Proposition 1. Given  and  , the Nash equilibrium abatement and output levels are given by
(i) If   c , then  0  1  1 and
ak c

q0  1  2

q   a  k  c
 1
1  2
(5)
(ii) If   c and    I , then  0  1, 1  0 and
  2c  a  k

q0 
1  2

q   a   k      c
1
1  2

(iii)
(6)
If   c and    I , then  0  0, 1  0 and
2  2  2    a  k

q0 
1  2




    k


a

q 
1
1  2

(7)
Substituting the optimal output and abatement levels in (5) - (7) back to (1) and (2), we obtain the
optimal profit and social welfare functions, denoted as ˆi ( , ), i=0,1 and Wˆ ( , ) . Note that
q0  q1 if   1: if the public firm cares only about its own profit, the equilibrium is symmetric
since the two firms have the same technologies. When   1 , the public firm differs from the private
firm in two aspects due to the former’s concern about social welfare: it might abate, and it tends to
8
produce more so as to raise consumer surplus. The two firms also respond differently to changes in
exogenous parameters. Proposition 2 highlights the differences for the case of Proposition 1(iii).
Proposition 2 Consider case (iii) of Proposition 1, i.e.,  0  0, 1  0 and q0 and q1 are given in
(7).
(i) Suppose   1 , i.e., the public firm cares about the social welfare. As pollution damage 
increases, the public firm’s output q0 decreases but the private firm’s output q1 increases.
(ii)As pollution tax  increases, the public firms’ output q0 decreases if   1/ 2 and the
private firms’ output q1 always decreases, and q1 decreases more than q0 does.
(iii)As consumer demand parameter a increases, both firms’ outputs rise, but the public firm’s
output rises more than that of the private firm.
(iv) As the marginal cost k rises, both firms’ outputs decrease, but the public firm’s output
decreases more than the private firm.
(v) As  increases, i.e., as the public firm cares more about its profit, the public firm’s output
q0 decreases, and the private firm’s output q1 increases.
When   1 , the public firm cares about the social welfare. Thus, as the pollution damage 
increases, the public firm reduces its output q0 but the private firm increases its output due to
strategic substitution between q0 and q1 . In general, the private firm produces less as tax increases,
but the public firm might produce more since the tax revenue is part of the social welfare. It will
produce less if it cares more about its profit, i.e., if   1/ 2 . When demand increases, both firms
produce more but since the marginal consumer surplus is higher, the public firm has incentive to
increase its output more than the private firm. When cost k rises, the fact that social welfare includes
both firms’ profits means that the public firm reduces its output more than the private firm. As 
increases, the public firm cares more about its profit and thus reduces its output q0 , and the private
firm increases its output q1 in response, mimicking results in the standard mixed oligopoly literature.
9
For cases (i) and (ii) of Proposition 1, the results in Proposition 2 (iii) – (v) remain valid: they
arise from the competitive incentives of the public firm and are independent of the abatement actions
of the firms. Results (i) and (ii) in Proposition 2 will be different: these results are about the effects of
pollution damage and tax, and the firms’ abatement behaviors are different across the three cases of
Proposition 1. Specifically, changes in pollution damage  have no effect on firm outputs in cases (i)
and (ii) of Proposition 1: the private firm does not care about pollution damage in choosing its output,
and the public firm fully abates its emissions so its output does not lead to any net emissions. As tax
 rises, the equilibrium outputs do not change in case (i) of Proposition 1 since both firms fully abate
so that neither pays the pollution tax. In case (ii) of Proposition 1, the private firm does not abate and
thus has to pay pollution tax, so that its output decreases in  . This, together with the fact that the
public firm fully abates, imply that the public firm’s output increases in  .
Stage 2: choice of  .The CEO chooses profit weight  to maximize his own payoff, knowing
the implications of this choice on the firms’ equilibrium output and abatement levels. The optimal 
chosen depends on the career choices of the CEO. If the CEO chooses a public career, it is obvious
that he would like the public firm to maximize social welfare. Thus, the CEO’s optimal choice in the
case of a public career is  G  0 . We let W * ( )  Wˆ ( G  0, ) denote the social welfare function
given that the CEO pursues a public career.
If the CEO pursues a private career, he chooses weight  to maximize  0  1 , knowing the
implications of his choice on the firms’ outputs and abatement levels given in Proposition 1. To
describe the CEO’s optimal decision, we first define several critical  functions. Specifically, let
1P ( )  arg max  (ˆ0 ( , )  ˆ1 ( , )) |
0  0,1  0

1 a  k  6  5
2 3  2a  2k  
be the CEO’s optimal choice of weight  given that neither firm abates, and
2P ( )  arg max  (ˆ0 ( , )  ˆ1 ( , )) |
0 1,1  0

1 a  k  4c  3
4 ak c
10
be the CEO’s optimal choice of weight  given that the public firm fully abates and the private firm
does not abate. The two critical weight functions are determined assuming fixed abatement behaviors;
of course, these behaviors will be induced in equilibrium by tax  and the CEO’s choice of  . It is
straightforward to verify that 1P ( )  2P ( )  1 / 4 for all   c , 1P ( ) /   0 , 2P ( ) /   0 , and
2P (  c)  1/ 4 . Further, let


3P ( )  max 2P ( ), ˆ ( ) ,
where ˆ ( ) is determined by (ˆ 0 (ˆ, )  ˆ1 (ˆ, )) |0 0,1 0  (ˆ 0 (2P ( ), )  ˆ1 (2P ( ), )) | 0 1,1 0 , i.e.,
ˆ ( ) is the value that equates the CEO’s payoff when the public firm is not abating with the payoff
when the public firm abates and   2P ( ) . Then the CEO’s optimal choice of weight  is given by
the following.
Proposition 3 Suppose the CEO pursues a private career.
(i) If   c , then the optimal weight is  P   / 4 .
(ii)If   c , then
(ii-a) If 1P   I , the optimal  P  1P and the public firm does not abate in stage three;
(ii-b) If 1P   I  3P , the optimal  P   I and the public firm does not abate in stage
three; and
(ii-c) If  I  3P , the optimal  P  2P and the public firm fully abates in stage three.
When   c , both the public and private firms fully abate. Our model falls back to a standard
mixed economy model with production costs being k   . To gain a larger market share and
competitive advantage, the public firm CEO has incentive to choose   1 since the firm with social
welfare considerations will produce more. The linearity assumptions then implies that  P   / 4 .
Figure 1 illustrates the optimal choice of  P when   c . The two payoff curves depict the CEO’s
payoff, f ( 0  1 ) , as a function of weight  given two fixed abatement levels of the public firm,
11
 0  1 and  0  0 respectively (with the private firm not abating). The CEO’s payoff is higher when
the public firm does not abate. The associated weights that maximize the payoffs are 1P and 2P
respectively. Of course, the public firm’s abatement level is not fixed but is induced by the value of
 (relative to  I ) according to Proposition 1 (ii) and (iii). The relevant payoffs are represented by the
bold curves, corresponding to the payoffs associated with  0  1 when    I and that associated
with  0  0 when    I . When 1P   I , Panel (a) shows that the optimal weight choice is 1P .
On the other hand, when  I  3P , the CEO’s relevant payoff is represented by the bold lines in
Panel (c), and it is obvious that the optimal weight is 2P . When 1P   I  3P , the CEO’s payoff is
represented by the bold lines in Panel (b) and the optimal weight is  I .
[Insert Figure 1 Here]
The positions of the threshold weights iP , i  1,..., 3 , and of  I relative to [1P , 3P ] , depend on
the tax level  . As the tax increases, not only will the values of the four threshold weights change, but
also their relative positions and thus which of them will be the one chosen by the CEO. There are
many configurations, sharing a common and significant pattern: as the tax rate increases, the optimal
weight might shift from one threshold value to another, leading to jumps in the public firm’s
abatement level and thus the payoffs. Below we illustrate one such case in Figure 2. As the tax
increases, the relative position of  I changes although the ranking of the other three threshold
weights remains unchanged. Consider first low tax levels,    1 where  1 is defined as the crossing
point of 1P ( ) and  I ( ) if it exists:  1  min   0, s.t.  I ( )  1P ( ) . In this case,
 I ( )  1P ( ) and from Proposition 3, the optimal weight is  P  1P ( ) and the public firm does
not abate. As the tax further increases so that 1     2 where  2 is such that  I ( 2 )  3P ( 2 ) ,
1P ( )   I ( )  3P ( ) and the optimal weight becomes  P   I ( ) , i.e., the CEO chooses weight
 I ( ) and the public firm does not abate. When the tax is sufficiently high so that  2    c ,
12
 I ( )  3P ( ) , the optimal weight jumps down to  P  2P ( ) and the public firm fully abates. Note
that, since lim c  I ( )  1 and 3P (c)  1 , we know  2  c . Finally, when   c , the optimal
 P  1 / 4 . The optimal weights when the CEO chooses a private career are depicted by the bold
curves in Figure 2.
[Insert Figure 2 Here]
As the tax increases, the private-career CEO tends to impose a higher weight on the private profit.
A “standard” result in the mixed economy literature is that even when the CEO cares only about the
private profit, he has incentive to impose a low profit weight so that the public firm can produce more
and thus capture a higher market share. Proposition 2 indicates that pollution tax plays a similar role:
when the tax rate increases, the public firm’s market share increases. As a result, when the tax
increases, there is less need for the CEO to impose a low weight in order to induce a higher market
share. A higher tax thus leads to a higher weight  and makes the public firm behaving more like a
private firm.
However, the effect of tax  on the CEO’s weight choice is discontinuous: the weight jumps
down at    2 and the public firm switches from no abatement to full abatement. A tax increase in
this case leads to a discontinuous decrease in pollution levels.
From Propositions 1-3, we know
Corollary 1. (i) If the CEO pursues a public career, in equilibrium  G  0 , 0  1 , and
1
0
1  
if   c
if   c
.
(ii) if the CEO pursues a private career, in equilibrium  P is given in Proposition 3. Further,
13
1
0
1  
if   c
if   c
1
and  0  
0
if    2
if    2
, where  2 is the crossing point of 1P ( )
and 3P ( ) .
Stage 1: the CEO’s career choice. Substituting the CEO’s optimal weight choices in Proposition
3 into profit functions ˆi ( , ), i  0,1 , we obtain the (reduced form) optimal profit functions given
that the CEO pursues a private career:  i* ( )  ˆi ( P ( ), ) , i  0,1 . We have defined the payoff
functions f () and g ( ) rather “generically,” characterizing them as being dependent on profit
difference  0  1 and social welfare W respectively. As we show below, this model enables us to
study how the profit difference and social welfare vary as pollution tax changes, and thus how the
exogenous parameter changes favor one career choice over the other. We choose not to explicitly
“anchor” the two payoff functions (e.g., by imposing specific intercept values of f and g when both
functions are linear). Instead, we only require that one payoff function do not completely dominate
the other for all parameter values, so that the career choice decision is not trivial.
II.2 Effects of pollution taxes
As we showed earlier, the pollution tax affects the choices of profit weights and abatement levels. We
next show how it affects the public firm CEO’s career choice.
Proposition 4. (i) When   c ,
W * ( )  ( 0* ( )   1* ( ))

 0 . In this case,  0  1  1 ,  P  1 / 4


and  G  0 : all pollution is abated and the tax has no effect on the firms’ profit levels or the social
welfare, and thus does not affect the public firm CEO’s career choice.
14
(ii) When  2    c ,
W * ( )  ( 0* ( )   1* ( )) 7

, and a tax increase tends to favor the private


career.
W * ( )  ( 0* ( )   1* ( )) 8

(iii) When 0    1 ,
, and a tax increase tends to favor the public


career.
(iv) When 1     2 , the relative effects of  on W * ( ) and  0* ( )   1* ( ) and thus on the
CEO’s career choice are ambiguous.
When the tax rate is high, both firms choose to fully abate, effectively paying no pollution tax.
Thus neither the welfare nor the relative profit is further affected as the environmental tax varies.
When the tax rate is lower so that  2    c , the public firm abates but the private firm does not
abate. Within this range, increase of the tax hurts the private firm, thus raises the relative profit for the
public firm. Further, a tax increase in this range results in higher deadweight loss due to lower output
levels, and thus hurts social welfare. Consequently a higher tax in this range favors the private career
more than the public career. When the tax rate is even lower so that 0    1 , neither firm abates. As
we showed earlier, a high tax in this case would reduce social welfare but reduces the relative profit
 0  1 even more than welfare since q0  q1 . A higher tax thus favors the public career. When the tax
rate is modest so that  1     2 , these two forces are almost balanced, resulting in ambiguous effects.
In summary, when the emission tax is low, further increases in the tax rate favor the public
career more than the private career. In other words, as the tax rate increases, it is possible that a CEO
who has chosen a private career switches to a public career. However, as the tax rate further increases,
Proposition 5(ii) indicates that the higher tax rate might favor the private career more than the public
7
To see this, note that
W *  ( 0*   1* )

 (a  k  t ) / 2  c  d  0 if  2    c .


8
To see this, note that
W *  ( 0*   1* )

 (a  k  t ) / 6  d  c  0 if 0    1 .


15
career. It is thus possible that the CEO will switch his career choice back to the private career. The
tax rates that can induce a public career tend to be in the “intermediate range.” Figure 3 (a) illustrates
this possibility: as emission tax increases, the ranking of payoffs from the two career choices changes
signs multiple times.
The effects of emission taxes on career choices have important implications for the total
emissions in the economy. In particular, when the CEO switches from a public career to a private
career, total emissions in the economy jump up. Figure 3(b) shows the changes in emission levels as
the tax rate increases. Given a fixed career choice, the total emission level is always decreasing in the
tax rate, and the emission levels associated with the public career lie below those of the private career
unless the tax rate   c . Shifts from public to private career always involve upward jumps in total
emissions. Thus, endogeneity of CEO’s career choices implies that the emission levels are not
monotonically decreasing in emission taxes anymore.
Figure 3(c) shows the net welfare effects of emission taxes. As expected, the social welfare
associated with a public career dominates that of a private career. Note that the welfare associated
with the private career is non-monotonic and discontinuous. For instance, when the tax levels are low,
neither the public nor the private firm abates. Emission tax does not affect the abatement level and is
distortionary, and thus reduces the social welfare. However, social welfare can jump when the
abatements of the firms change. More importantly, Figure 3(c) shows that welfare levels can jump
down as the tax rate increases if it causes the public firm’s CEO to switch from a public to a private
career. Given that a public career welfare-dominates a private career, and in light of Proposition 5, the
optimal tax rates tend to be in the intermediate range. Specifically, it tends to be below the Pigouvian
tax rate of    .
[Insert Figure 3 Here]
III. Emission Standard
In this section we study the effects of emission standards. We consider a particular form of
standard, namely the proportion of emissions that a firm has to abate. Let   [0,1] be the standard,9
9
We assume a  k  3
 2  0 so that all equilibrium outputs are nonnegative.
16
representing the proportion of a firm’s emissions that has to be abated. If a firm’s output (and thus its
gross emission) is q, its net emission level under this standard is (1   )q .
III.1 Subgame perfect Nash equilibrium
Similar to the case of pollution taxes, we use backward induction to find the subgame perfect
Nash equilibrium under standards. The analysis is similar, so are most of the results. In stage 3, given
standard  and weight  , the public and private firms engage in Cournot competition. Since the
private firm only cares about its profit, it always abates up to the standard: 1   . The public firm’s
abatement choice depends on its profit weight. Similar to the case of pollution tax, there exists a
 c
threshold weight level  I 
such that when    I , the public firm is indifferent between fully

abating and abating up to the standard. In this case we assume that the public firm abates only up to
the standard. It fully abates only if it cares sufficiently strongly about the social welfare, i.e., if
   I . The following results are parallel to Proposition 1.
Proposition 5. Given standard  and weight  , in the Nash equilibrium the private firm always
abates up to the standard. Further,
(i) If    I , the public firm fully abates ( 0  1) and the outputs are given by

c  2c  a  k
q0 

1  2

q   a   k   c  c  c
 1
1  2
(8)
(ii)If    I ,  0   and the equilibrium outputs are

2  2  2  2  a  k  c
q0 
1  2

q     a   k   c      
 1
1  2
(9)
Substituting the optimal output and abatement levels in (8) and (9) back to (1) and (2), we
17
obtain the optimal profit and social welfare functions, denoted as i ( ,  ), i=0,1 , and W ( ,  ) .
Similar to the case of taxes, when the public firm fully abates, further tightening of the standard
(increasing  ) only hurts the private firm since it will have to abate more. Thus in (8), q0 is
increasing while q1 is decreasing in standard  . When both firms are constrained by the standard,
the private firm’s output is always decreasing in the standard, again since it cares only about its profit
and abatement is costly. Even though the standard is binding for the public firm, the public firm’s
output can still be increasing in the standard as long as its profit weight is not too high: a sufficient
condition for this to be true is   1/ 2 .
The CEO again chooses the profit weight in order to influence the firms’ decisions. Similar to
the case of pollution tax, if the CEO chooses a public career, the optimal profit weight is  G  0 . The
private career CEO’s optimal choice of weight  P again depends on the comparisons of several
critical weight levels. Parallel to the case of emission taxes, let
1P ( )  arg max  (0 ( ,  )  1 ( ,  )) |
0  ,1 

1 a  k  6  c  6
2 3  2a  2k  2c  3
be the CEO’s optimal choice of weight  given that both firms abate up to the standard, and
2P ( )  arg max  (0 ( , )  1 ( , )) | 1,  
0
1
1 a  k  4c  3c
4
ak c
be the CEO’s optimal choice of weight  given that the public firm fully abates and the private firm
abates only up to the standard. It is straightforward to verify that 1P ( ) /   0 , 2P ( ) /   0 ,
and 1P ( )  2P ( )  1 / 4  1P (1)  2P (1) for all   1 . Further, let
3P ( )  max 2P ( ),  ( ) ,
where  ( ) is determined by ( 0 (,  )  1 (,  )) |0  ,1   ( 0 (2P ( ),  )  1 (2P ( ),  )) |0 1,1  .
Then the private career CEO’s optimal choice of weight  P is given by
18
Proposition 6 Suppose the CEO pursues a private career.
(i) If  I  1P ( ) , the optimal  P ( )  1P ( ) and the public firm abates at the required
level  in stage three;
(ii) If 1P ( )   I  3P ( ) , the optimal  P ( )   I ( ) and the public firm abates at the
required level  in stage three; and
(iii) If  I  3P ( ) , the optimal  P ( )  2P ( ) and the public firm fully abates in stage
three.
Substituting the optimal choice of  G  0 into the social welfare function W ( ,  ) , we obtain the
(reduced form) optimal social welfare when the CEO pursues a public career: W * ( )  W ( G  0,  ) .
Substituting the optimal choices of  P in Proposition 6 into the profit functions i ( ,  ), i=0,1 , we
obtain the (reduced form) optimal profit functions when the CEO pursues a private career:
i* ( )  i ( P ( ),  ) , i=0,1. Again, parallel to the case of pollution tax, the positions of the
threshold weights iP , i  1, 2, 3 , and of  I relative to [1P , 3P ] , depend on the parameter values
including standard  . As the standard increases, not only will the values of the four threshold
weights change, but also their relative positions and thus which of them will be the one chosen by the
CEO. Figure 4 illustrates two possible patterns, one involving jumps in the optimal weights and the
other involving smooth changes in  P .
In Figure 4, the three threshold curves, 1P ( ) , 2P ( ) , and 3P ( ) , cross at   1 (taking the
value of ¼), while  I is independent of  . In Figure 4 (a),  I ( )  1/ 4 , which is equivalent to
  4c / 3 , a case of low pollution damage. Then for low standard levels,  P   I ( ) and for high
standard levels,  P  1P ( ) . In both cases the public firm abates at level  in stage three. In Figure
4 (b),  I ( )  1/ 4 , which is equivalent to   4c / 3 , a case of high pollution damages. Then at low
standard levels,  P   I ( ) and the public firm abates at level  in stage three. But at high
19
standard levels, the value of  P jumps down to  P  2P ( ) and the public firm fully abates in stage
three. Similar to the case of emission taxes, the private career CEO’s profit weight is non-decreasing
in the standard when there are no jumps: as the government tightens the standard, the CEO responds
by behaving more like a private firm.
[Insert Figure 4 Here]
Figure 4, together with Propositions 5 and 6, shows that when the CEO pursues a private career,
there is only one case when the public firm fully abates: when   1 in Figure 4(b). In this case,
 P  2P (cf. Proposition 6(iii)) and since 2P   I ,  0  1 (cf. Proposition 5(i)). Let
1  {  0, s.t.  I  3P ( ) |   4c / 3} (cf. Figure 4(b)). Then
Corollary 2. (i) If the CEO chooses a public career, in equilibrium 0  1 and 1   .
(ii) If the CEO chooses a private career, in equilibrium 1   , and
1
0  

if   4c/3 and   1
otherwise
.
III.2. Effects of emission standards
The effects of the emission standard are structurally similar to those of the emission tax. As the
standard tightens, the CEO’s career objective may change, and given a fixed career objective, his
choice of the profit weight may also change. Both will lead to changes in output and abatement levels.
Let  2  {  [0,1], s.t.  I  1P ( ) |   4c / 3} (cf. Figure 4(a)). Proposition 7 shows how the CEO’s
career choice is affected by the standard.
Proposition 7. (i) If   4c / 3 and   1 , then
 ( 0* ( )  1* ( )) W * ( )

: a stricter standard


favors the private career;
20
(ii) If   4c / 3 and    2 , then
 ( 0* ( )  1* ( )) W * ( )

: a stricter standard favors the


public career;
(iii) In other cases, the relative effect of standard  on profit difference  0* ( )  1* ( ) vs. on
social welfare W * ( ) is ambiguous.
Proposition 7 indicates that the effects of the standard depends on the damage level  . When the
pollution damage is high (case (i)), the public firm always fully abates regardless of the CEO’s career
choice. Stricter standards only hurt the private firm, thereby increasing the profit difference, and thus
favors private career. When the damage is low (case (ii)), the public firm does not fully abate when
the CEO chooses a private career. In this case, stricter standards hurt both the public and private firm,
making the private career less attractive compared with the public career.
Similar to the case of emission taxes, the endogeneity of the CEO’s career choice can lead to
non-monotonic effects of emission standards on net pollution levels. Figure 5 shows an example with
  4c / 3 , so that as the standard tightens, the CEO switches from a public to a private career (Panel
(a)). Although the pollution level decreases as the standard tightens for a fixed career objective
(bottom line for public career and top lines for private career), the switch in the CEO’s career
objective leads to a dramatic increase in pollution (panel (b)).
[Insert Figure 5 Here]
Figure 5(c) illustrates the effects of emission standards on social welfare. When the CEO
pursues a public career, a higher standard always improves social welfare (top line in Panel (c)).
Since the public firm always fully abates (since  G  0 ), the only effect of raising the standard is to
force the private firm to abate more. Since abatement is socially desirable, this tends to improve
social welfare. Further, although the private firm reduces its output in response to the higher standard
(and thus higher levels of abatement), as shown in (8), the lost output is entirely (and exactly) made
up by the increased production of the public firm. The total output is thus unchanged, so is the
consumer surplus. As a result, the social welfare is always increasing in the stringency level of the
21
standard. However, when the CEO pursues a private career, a higher standard might not always
improve social welfare (bottom line in Panel (c)). Although more stringent standard always reduces
pollution (from the private firm and sometimes from the public firm when a0   ), it can also reduce
the total output level, aggravating the loss in consumer surplus due to imperfect competition. A key
observation in Figure 5 (c) is that social welfare under the public career is always higher than that
under the private career.
Given the welfare dominance of the public career over the private career, Proposition 7 and
Figure 5 show that the socially optimal standard might be far below the first best case of full
abatement. For pollution intensive industries, the public firm already fully abates and stricter
standards will hurt the private firm only, thereby driving up the profit difference between the two
firms and making the private career more attractive. A relatively loose standard might thus be optimal
for pollution intensive industries while a tighter standard might be optimal for less pollution intensive
industries (Proposition 7(ii)). What drives these counter-intuitive findings is the endogeneity of the
public firm CEO’s career choices and thus the public nature of the firm itself.
IV. Comparison: Tax vs. Standard
A standard result in the environmental economics literature is that, with symmetric firms and
without uncertainties, information asymmetries or transaction costs, emission taxes and standards are
equivalent: for any tax, there is a standard that leads to the same pollution levels and vice versa.
When the firms are heterogeneous, a uniform tax is advantageous over a uniform standard since the
former equates the marginal abatement costs of the firms. In our model, the public and private firms
share the same abatement and production technologies. Their difference lies in the divergent objective
functions arising from the nature of mixed economies, and we show in this section that the
equivalence between taxes and standards breaks down. When this happens, we further identify the
“better” regulatory tool, which may not always be emission taxes.
Figures 6 and 7 show two examples of “anchored” comparisons of taxes and standards for two
different scenarios. On the horizontal axis, tax  goes from zero to one, so does standard  . Note
that there is no regulation on emissions when  and  are both zero, and there is full regulation
22
(full abatement) when they are both one. The two end values of zero and one thus provide natural
anchors when comparing the effects of the two policies. For instance,     0.4 represent
regulations that are 40% stringent compared with the “full regulation” associated with each policy
instrument.
Panel (a) in each of Figures 6 and 7 shows the impacts on total emission levels and Panel (b)
shows the impacts on welfare. Thick curves are associated with emission standards while thin curves
are for emission taxes. Solid lines represent the realized emission levels or welfare when the CEO’s
career objective is endogenously chosen, while dotted lines represent the emission and welfare levels
for fixed careers.
[Insert Figure 6 Here]
[Insert Figure 7 Here]
Panels (a) in both Figures 6 and 7 demonstrate the breakdown of the equivalence between taxes
and standards. Specifically, the CEO’s career endogeneity causes jumps in realized emission levels,
and in the case of emission taxes, the jumps lead to ranges of emission levels that are not achievable
under taxes. For instance, emission at E=2 in Figure 6(a) can be induced by a standard of   0.4 ,
but there does not exist an equivalent tax that can induce this level of total emissions.
Panels (b) in both figures show that there is not a clear dominance relationship between taxes
and standards. There are ranges of regulation levels where taxes dominate standards, and other ranges
where the dominance relation is reversed. However, a consistent pattern is that, quite intuitively, a
policy tends to be dominant if it induces a public career while the other policy induces a private career.
For instance, in Figure 7(b), welfare associated with low levels of standards that induce a public
career is higher than that associated with (higher levels of) taxes and standards that induce a private
career. Similarly, welfare associated with taxes that induce a public career dominates that associated
with both policies when they induce a private career. Thus, the determining factor in welfare rankings
of the policies lies in the career objectives that they induce. A policy instrument tends to be effective
if it induces a public career. Ultimately, the optimal policy choice in Figure 6 is a tax at the level of
 *  0.84 , while the optimal policy choice in Figure 7 is a standard at the level of  *  0.81.
23
V. Discussion and Conclusions
In this paper, we study environmental regulation in mixed economies where public and private
firms engage in Cournot competition, and show that some fundamental results in environmental
economics, such as the equivalence between taxes and standards, fail to hold in these economies. This
is important given the pervasive nature of mixed economies in developing countries and in many
industrialized nations. Public firms behave differently from private firms since their behaviors are not
entirely profit driven. However, as we argue and model in this paper, their objectives are not
necessarily fixed. Instead, they are influenced by the CEO’s career choices, and both the CEO’s
career choices and the public firm’s objectives are affected by environmental regulation, including the
stringency and specific instruments of the regulation.
The endogenous career choices of the CEO drive much of the “non-standard” effects of
environmental regulation. More stringent regulation does not necessarily lead to less pollution, since
it might induce the CEO to switch from a public career to a private career, causing upward jumps in
pollution levels. In fact, the optimal emission tax is typically lower than Pigouvian tax, and the
optimal emission standard might be lower when the sector is more pollution intensive compared with
a less pollution intensive sector. There is no clear dominance relation between taxes and standards,
with the instrument that induces a public career being more likely to be welfare dominant. These
results highlight an important phenomenon that has not been modeled in the literature: environmental
regulation can affect not only the firms’ payoffs but also their objective functions. The endogenous
payoff functions are similar in spirit to the endogenous preference literature (Bowles, 1998), where
government regulation might alter the preferences of individuals. Our paper presents a structural
model of how firm preferences can be altered through the CEO’s career choices, and shows how this
endogeneity can lead to questions about some “standard” conclusions in environmental economics.
Although we model strategic interactions between public and private firms as Cournot, our
results are robust to other strategic interactions such as the public firm being the Stackelberg leader.
This is intuitive: different career choices of the CEO will inevitably lead to discrete changes in the
public firm’s weighting between profit and social welfare, which in turn will lead to jumps in
emission and welfare levels. The forms of strategic interactions between public and private firms
24
might affect the magnitude and location but not the existence of the discontinuities. Similarly, our
results are also robust to the linear quadratic setup. Even with convex production costs and a
nonlinear demand function, the discontinuity in policy levels and instrument choices due to the
discrete career choices can still lead to jumps in emission and welfare levels.
References
Barros, Fatima.: 1995. Incentive Schemes as Strategic Variables: An Application to a Mixed
Duopoly, International Journal of Industrial Organization13: 373-386.
Bowles, Samuel. :1998. Endogenous Preferences: The Cultural Consequences of Markets and
other Economic Institutions, Journal of Economic Literature XXXVI: 75-111.
Chang, Y-C and Wang, N.: 2010. Environmental regulations and emissions trading in China,
Energy Policy 38: 3356-3364.
Darnall, N. and Edwards, D. : 2006. Predicting the cost of environmental management system
adoption: the role of capabilities, resources and ownership structure. Strategic Management Journal,
27: 301–320.
DeFraja, G. and Delbono, F.: 1989. Alternative Strategies of a Public Enterprise in Oligopoly,
Oxford Economic Papers 41: 302-311.
Du, N., Heywood, J. S., and Ye, G.: 2013. Strategic Delegation in an Experimental Mixed
Duopoly, Journal of Economic Behavior and Organization 87: 91-100.
Endres, A.: 1997. Negotiating a Climate Convention—The Role of Prices and Quantities.
International Review of Law and Economics 17: 147-156.
Endres, A. and M. Finus,: 2002. Quotas May Beat Taxes in a Global Emission Game.
International Tax and Public Finance, 9: 687-707.
Fjell, K. and Heywood, J. S.: 2004. Mixed Oligopoly, Subsidization and the Order of Firm's
Moves: The Relevance of Privatization, Economics Letters 83: 411-416.
Grossman, G. M. and Krueger, A.: 1995. Economic Growth and the Environment, Quarterly
Journal of Economics 112: 353-377.
Hambrick, D. C. and Finkelstein, S.: 1987. Managerial discretion: A bridge between polar views
of organizational outcomes, Research in Organizational Behavior 9: 369–406.
Hambrick, D. C. and Abrahamson, E,: 1995. Assessing managerial discretion across industries:
a multimethod approach. Academy of Management Journal 38: 1427-1441.
25
Hanh, R. W.: 2000. The Impact of Economics on Environmental Policy, Journal of
Environmental Economics and Management 39: 375-399.
Heywood, J. S., and Ye, G.: 2009. Mixed Oligopoly, Sequential Entry and Spatial Price
Discrimination, Economic Inquiry 47: 589–597.
Jaffe, A.B. and Stavins, R.: 1995. Dynamic incentives of environmental regulations: the effects
of alternative policy instruments on technology diffusion, Journal of Environmental Economics and
Management, 29: S43-S63.
Jansen, T., Lier, A. V. and Witteloostuijn, A. V. :2007. A note on strategic delegation: The
market share case," International Journal of Industrial Organization 25: 531-39.
Jung, C., Krutilla, K. and Boyd, R.: 1996. Incentives for advanced pollution abatement
technology at the industry level: an evaluation of policy alternatives, Journal of Environmental
Economics and Management, 30: 95-111.
Mascarenhas B. :1989. Domains of state-owned, privately held, and publicly traded firms in
international corporations, Administrative Science Quarterly 34: 582–597.
Matsumura, Toshihiro: 1998. Partial Privatization in Mixed Duopoly, Journal of Public
Economics70: 473 – 483.
Matsumura, T.: 2003. Endogenous Role in Mixed Markets: a Two Production Period Model,
Southern Economic Journal 70: 403–413.
Montero, J. P.: 2002. Prices versus quantities with incomplete enforcement, Journal of Public
Economics 85: 435-454.
Pal, D.: 1998. Endogenous Timing in a Mixed Oligopoly, Economics Letters, 61: 181–185.
Sawhney, A.: 2004. The new face of environmental management in India. Ashgate Publishing
Company. VT: Burlington.
Shleifer, A., Vishny, R.: 1994. Politicians and firms. Quarterly Journal of Economics 109:
995–1025.
Stavins, R. N.: 2003. Experience with market-based environmental policy instruments, in Maler,
K.G. and J.R. Vincent eds. Handbook of Environmental Economics, vol 1, Chapter 9, pp 355-435.
White, M.D.: 2001. Managerial Incentives and the Decision to Hire Managers in Markets with
Public and Private Firms, European Journal of Political Economy 17: 877 – 896.
White, M.D.: 2002. Political Manipulation of A Public Firm's Objective Function, Journal of
Economic Behavior and Organization 49: 487 – 499.
26
Zeckhauser, R.J., Horn, M.,: 1989. The control and performance of state-owned enterprises. In:
MacAvoy, P.W., et al. (Eds.), Privatization and State-Owned Enterprises: Lessons from the United
States, Great Britain and Canada. Kluwer Academic Publishers, Boston, pp. 7–57.
Zhao, J.: 2003. Irreversible Abatement Investment under Cost Uncertainties: Tradable Emission
Permits and Emissions Charges, Journal of Public Economics, 87: 2765-2789.
27
Figure 1. Optimal choice of profit weight λ P when τ < c
(a)
(b) :
λ1P < λ I ≤ λ3P
λ1P ≥ λ I
(c):
λ I > λ3P
28
Figure 2. Optimal weight  P as a function of tax 
29
Figure 3. Effects of emission taxes
(a) Career choices
Private career
Public career
Public career
Private career
(b) Emissions
(c) Welfare
Note: parameter values used are a  5.5, k  1, c  0.9,   1 .
30
Figure 4. Effects of standard  on profit weight  P
(a)
  4c / 3
(b)
  4c / 3
31
Figure 5. Effects of emission standards on career choices, pollution and welfare.
(a) Career choices
Public career
Private career
Private career
Public career
(b) Emissions
Note: parameter values used are a  5.5, k  1, c  0.6,   1 .
(c) Welfare
32
Figure 6. Comparison of taxes and standards: scenario I
 *  0.84
(a) Impacts on total emissions
(b) Impacts on welfare
Graph Legend:
Unrealized values associated with Standard
Unrealized values associated with Tax
Realized values associated with Standard
Realized values associated with Tax
Note: parameter values used are a  5.5, k  1, c  0.9,   1 .
33
Figure 7. Comparison of taxes and standards: scenario II
 *  0.81
(a) Impacts on total emissions
Graph legend:
Unrealized values associated with Standard
Unrealized values associated with Tax
(b) Impacts on welfare
Realized values associated with Standard
Realized values associated with Tax
Note: parameter values used are a  5.5, k  1, c  0.6,   1 .
34